Cross product
Overview

In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the cross product, vector product, or Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

vector product
is a binary operation
Binary operation
In mathematics, a binary operation is a calculation involving two operands, in other words, an operation whose arity is two. Examples include the familiar arithmetic operations of addition, subtraction, multiplication and division....

on two vectors in three-dimensional space
Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...

. It results in a vector which is perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

to both of the vectors being multiplied and normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

to the plane containing them. The name "cross product" is derived from the cross symbol
×
The multiplication sign is the symbol ×. The symbol is similar to the lowercase letter x but is a more symmetric saltire, and has different uses. It is also known as St...

"" that is often used to designate this operation; the alternative name "vector product" emphasizes the vector (rather than scalar
Scalar (mathematics)
In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector....

) nature of the result.